[beagle3]

“Characterstic function” is (was) an overloaded term.

What you described is more often referred to as an “indicator function” these days, with “characteristic functions” denoting the transform (Fourier, laplace, z - depending on context). Closely related to “moment generating functions” to the point of being almost interchangeable.

[ysofunny]

so the same thing but, characterisic function as I knew them before these posts is a rudimentary 2-variable finite version. point and line (but the line is a curve, a circle because e).

but the new and improved 21st century characteristic functions are n-variable and have a full continious spectrum of variables between zero (false) and one (true) but only potentially lest infinite realizes itself (which would make the theories illogical).

this way of thinking about this makes sense to me, even if it's ever so slighly wrong by some nitpickable point https://en.wikipedia.org/wiki/Moment-generating_function